Finite Group Databasebeta

← #11884520

Subgroups — #11884520

Order 1152.

1434 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#547C211yesmaximal, characteristic, complemented
2C2×#64160C211yesmaximal, characteristic, complemented
3C2×#64159C211yesmaximal, characteristic, complemented
4#10596023C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6#10592937C211yesmaximal, characteristic, complemented
7#10592789C211yesmaximal, characteristic, complemented
8#10592785C211yesmaximal, characteristic, complemented
9#10592750C211yesmaximal, characteristic, complemented
10#10592749C211yesmaximal, characteristic, complemented
11#10592748C211yesmaximal, characteristic, complemented
12#10592746C211yesmaximal, characteristic, complemented
13#10592717C211yesmaximal, characteristic, complemented
14#10592715C211yesmaximal, characteristic, complemented
15#10592710C211yesmaximal, characteristic, complemented
16#83528—34nomaximal
17C2×C32×#41C2211yescharacteristic
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic
22C32×#123—21no—
23C32×#123—21no—
24C32×C22⋊Q8C2211yescharacteristic
25C32×C22⋊Q8C2211yescharacteristic
26C32×#121—21no—
27C32×C4×D4C2211yescharacteristic
28C32×C4×D4C2211yescharacteristic
29C2×C32×C4⋊C4—21no—
30#64160—24no—
31#64159—24no—
32C2×#3756C2211yescharacteristic
33C2×#3756C2211yescharacteristic
34C2×#3756C2211yescharacteristic
35C2×#3756C2211yescharacteristic
36C2×#3755C2211yescharacteristic
37C2×#3755C2211yescharacteristic
38#64148—21no—
39C2×#3754C2211yescharacteristic
40C2×#3754C2211yescharacteristic
41C2×#3753C2211yescharacteristic
42#64139C2211yescharacteristic
43#64133C2211yescharacteristic
44C2×#3748C2211yescharacteristic
45C22×C3⋊(C3⋊C8)C2211yescharacteristic
46#64105—21no—
47#64094—21no—
48#64090—21no—
49#64084C2211yescharacteristic
50C4×#634C2211yescharacteristic
51#63662C2211yescharacteristic
52#63662C2211yescharacteristic
53#63659C2211yescharacteristic
54#63657C2211yescharacteristic
55#63657C2211yescharacteristic
56#63637C2211yescharacteristic
57#63637C2211yescharacteristic
58#63636C2211yescharacteristic
59#63634C2211yescharacteristic
60C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
61#63630C2211yescharacteristic
62C3×#547D314yescomplemented
63C2×#951—34no—
64C2×#950—34no—
65#5552—34no—
66#5239—34no—
67#5238—34no—
68#5090—34no—
69#5086—34no—
70#5051—34no—
71#5050—34no—
72#5049—34no—
73#5047—34no—
74#5018—34no—
75#5016—34no—
76#5011—34no—
77C32×#41—22no—
78C32×#41—22no—
79C32×#41—41no—
80C32×#41—41no—
81C2×C32×Q8C2311yescharacteristic
82C2×C32×Q8C2311yescharacteristic
83C2×C32×D4—21no—
84C2×C32×D4—21no—
85C2×C32×D4D411yescharacteristic
86C2×C32×D4C2311yescharacteristic
87C22×C32×C4—21no—
88C22×C32×C4—21no—
89C22×C32×C4—21no—
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C2×#638—21no—
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634—22no—
100C2×#634—21no—
101C2×#634—41no—
102C2×#634C2311yescharacteristic
103C2×#634C2311yescharacteristic
104C32×C4⋊C4—21no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4—21no—
107C32×C4⋊C4—21no—
108C32×C4⋊C4D411yescharacteristic
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111C32×C22⋊C4—21no—
112C32×C22⋊C4—21no—
113C32×C22⋊C4D411yescharacteristic
114C32×C22⋊C4D411yescharacteristic
115C32×C42C2311yescharacteristic
116#3757—21no—
117#3756—22no—
118#3756—22no—
119#3756—22no—
120#3756—41no—
121#3755—22no—
122#3755—41no—
123#3754—22no—
124#3754D414yescomplemented
125#3753—22no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131#3750—21no—
132C4×C3⋊Dic3—21no—
133#3748—22no—
134C2×C3⋊(C3⋊C8)—22no—
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139#3269—91noSylow
140C2×C3×#41C2×D314yes—
141C2×C3×#41C2×D314yes—
142C2×#235—34no—
143C22×Dic6—34no—
144C3×C4⋊Q8C2×D314yes—
145C3×#123—24no—
146C3×#123—24no—
147C3×C22⋊Q8C2×D314yes—
148C3×C22⋊Q8C2×D314yes—
149C3×#121—24no—
150C3×C4×D4C2×D314yes—
151C3×C4×D4C2×D314yes—
152C2×C3×C4⋊C4—24no—
153#951—616no—
154#950—616no—
155C2×#216—34no—
156C2×#216—34no—
157C2×#216—34no—
158C2×#216—34no—
159C2×#215—34no—
160C2×#215—34no—
161#939—64no—
162C2×#214—34no—
163C2×#214—34no—
164C2×#213—34no—
165#930—34no—
166#924—34no—
167C2×#208—34no—
168C22×C3⋊C8—34no—
169#896—64no—
170#885—64no—
171#67⋊C4—64no—
172#875—34no—
173C4×Dic6—34no—
174#835—34no—
175#835—34no—
176#832—34no—
177#830—34no—
178#830—34no—
179#810—34no—
180#810—34no—
181#809—34no—
182#807—34no—
183C4⋊(C3⋊C8)—34no—
184#803—34no—
185C23×C32—21no—
186C23×C32C2×D411yescharacteristic
187C23×C32C2×D411yescharacteristic
188C22×C3⋊D3—21no—
189C32×Q8—21no—
190C32×Q8—21no—
191C32×Q8—21no—
192C32×Q8—21no—
193C32×D4—21no—
194C32×D4—41no—
195C32×D4—42no—
196C32×D4—42no—
197C32×D4C2×D412yes—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—21no—
203C2×C32×C4—21no—
204C2×C32×C4—21no—
205C2×C32×C4—42no—
206C2×C32×C4—42no—
207C2×C32×C4—42no—
208C2×C32×C4C2×D411yescharacteristic
209C2×C32×C4C2×D411yescharacteristic
210C2×C32×C4C2×D411yescharacteristic
211C2×C32×C4C2×D411yescharacteristic
212C2×C32×C4C2411yescharacteristic
213#638—42no—
214#638—42no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—42no—
219C4⋊(C3⋊D3)—21no—
220C4⋊(C3⋊D3)—21no—
221C4×C3⋊D3—42no—
222#634—21no—
223#634—21no—
224#634—21no—
225#634—42no—
226#634C2×D412yes—
227C3⋊(C3⋊C8)—21no—
228C3⋊(C3⋊C8)—21no—
229C3⋊(C3⋊C8)—21no—
230C3⋊(C3⋊C8)C2×D412yes—
231C2×#137—91no—
232C2×#135—91no—
233#548—91no—
234#547C3⋊D311yescharacteristic, complemented
235#497—91no—
236#468—91no—
237#467—91no—
238#463—91no—
239#462—91no—
240#452—91no—
241#452—91no—
242#451—91no—
243#449—91no—
244#440—91no—
245#435—91no—
246C3×#41—28no—
247C3×#41—28no—
248C3×#41—44no—
249C3×#41—44no—
250C2×C3×Q8C22×D314yes—
251C2×C3×Q8C22×D314yes—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4#6714yes—
255C2×C3×D4C22×D314yes—
256C22×C3×C4—24no—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4C22×D314yes—
260C22×C3×C4C22×D314yes—
261C2×#67—64no—
262C2×#67—64no—
263C22×Dic3—64no—
264#235—68no—
265#235—124no—
266C2×D12—34no—
267C2×C4×D3—64no—
268C2×Dic6—34no—
269C2×Dic6—34no—
270C2×Dic6—68no—
271C2×Dic6—64no—
272C2×Dic6—124no—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—24no—
277C3×C4⋊C4#6714yes—
278C3×C4⋊C4C22×D314yes—
279C3×C22⋊C4—24no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—24no—
282C3×C22⋊C4#6714yes—
283C3×C22⋊C4#6714yes—
284C3×C42C22×D314yes—
285#217—64no—
286#216—68no—
287#216—68no—
288#216—68no—
289#216—124no—
290#215—68no—
291#215—124no—
292#214—316no—
293#214—68no—
294#213—68no—
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4—64no—
297(C2×D3)⋊C4—64no—
298C4⋊Dic3—34no—
299Dic3⋊C4—64no—
300Dic3⋊C4—64no—
301C4×Dic3—64no—
302#208—68no—
303C2×C3⋊C8—34no—
304C2×C3⋊C8—34no—
305C2×C3⋊C8—34no—
306C2×C3⋊C8—34no—
307C2×C3⋊C8—68no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—22no—
311C22×C32—21no—
312C22×C32—21no—
313C22×C32—21no—
314C22×C32—21no—
315C22×C32—41no—
316C22×C32—41no—
317C22×C32C22×D411yescharacteristic
318C2×C3⋊D3—41no—
319C2×C3⋊D3—41no—
320C2×C3⋊D3—41no—
321C32×C4—21no—
322C32×C4—21no—
323C32×C4—21no—
324C32×C4—21no—
325C32×C4—41no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4C22×D411yescharacteristic
329C32×C4H(5,𝔽2)11yescharacteristic
330C3⋊Dic3—22no—
331C3⋊Dic3—41no—
332C3⋊Dic3—41no—
333C2×#41—91no—
334C2×#41C2×C3⋊D311yescharacteristic
335C2×#41C2×C3⋊D311yescharacteristic
336C22×Q8—91no—
337#137—184no—
338#135—184no—
339C2×Q16—91no—
340C2×Q16—91no—
341C2×Q16—91no—
342C2×Q16—91no—
343C2×SD16—91no—
344C2×SD16—91no—
345C2×SD16—91no—
346C2×SD16—91no—
347C2×D8—91no—
348C2×M16—91no—
349C22×C8—91no—
350C4⋊Q8C2×C3⋊D311yescharacteristic
351#124—91no—
352#124—181no—
353#123—21no—
354#123—21no—
355C22⋊Q8—91no—
356C22⋊Q8—181no—
357C22⋊Q8C2×C3⋊D311yescharacteristic
358C22⋊Q8C2×C3⋊D311yescharacteristic
359#121—21no—
360#121—91no—
361#121—181no—
362C4×Q8—91no—
363C4×D4—181no—
364C4×D4C2×C3⋊D311yescharacteristic
365C4×D4C2×C3⋊D311yescharacteristic
366C2×C4⋊C4—21no—
367#107—91no—
368C4⋊C8—91no—
369#103—91no—
370#103—91no—
371#103—91no—
372#103—91no—
373#102—91no—
374#102—91no—
375C22⋊C8—91no—
376C22⋊C8—91no—
377#97—91no—
378C23×C3—24no—
379C23×C3C2×#6714yes—
380C23×C3C2×#6714yes—
381C22×D3—64no—
382C3×Q8—24no—
383C3×Q8—24no—
384C3×Q8—24no—
385C3×Q8—24no—
386C3×D4—24no—
387C3×D4—44no—
388C3×D4—48no—
389C3×D4—48no—
390C3×D4D3×D418yes—
391C2×C3×C4—24no—
392C2×C3×C4—24no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—24no—
397C2×C3×C4—24no—
398C2×C3×C4—48no—
399C2×C3×C4—48no—
400C2×C3×C4—48no—
401C2×C3×C4C2×#6714yes—
402C2×C3×C4C2×#6714yes—
403C2×C3×C4C2×#6714yes—
404C2×C3×C4C2×#6714yes—
405C2×C3×C4C23×D314yes—
406#67—128no—
407#67—128no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—64no—
411C2×Dic3—128no—
412D12—64no—
413D12—64no—
414C4×D3—128no—
415Dic6—38no—
416Dic6—64no—
417Dic6—64no—
418Dic6—64no—
419Dic6—128no—
420C3⋊C8—38no—
421C3⋊C8—64no—
422C3⋊C8—64no—
423C3⋊C8—64no—
424C2×C32—41no—
425C2×C32—41no—
426C2×C32—42no—
427C2×C32D4211yescharacteristic
428C2×C32#57511yescharacteristic
429C2×C32#57811yescharacteristic
430C3⋊D3—81no—
431#41—22no—
432#41—22no—
433#41—41no—
434#41—41no—
435#41—182no—
436#41—361no—
437C2×Q8—91no—
438C2×Q8—91no—
439C2×Q8—182no—
440C2×Q8—181no—
441C2×Q8—361no—
442C2×Q8C22×C3⋊D311yescharacteristic
443C2×Q8C22×C3⋊D311yescharacteristic
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—91no—
447C2×D4—181no—
448C2×D4—181no—
449C2×D4#63811yescharacteristic
450C2×D4C22×C3⋊D311yescharacteristic
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—181no—
455C22×C4—181no—
456C22×C4C22×C3⋊D311yescharacteristic
457C22×C4C22×C3⋊D311yescharacteristic
458Q16—182no—
459Q16—182no—
460Q16—182no—
461Q16—361no—
462SD16—94no—
463SD16—182no—
464SD16—182no—
465SD16—361no—
466D8—182no—
467M16—182no—
468C2×C8—91no—
469C2×C8—91no—
470C2×C8—91no—
471C2×C8—91no—
472C2×C8—182no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—91no—
478C4⋊C4—181no—
479C4⋊C4—181no—
480C4⋊C4#63811yescharacteristic
481C4⋊C4C22×C3⋊D311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—181no—
486C22⋊C4—181no—
487C22⋊C4—181no—
488C22⋊C4—181no—
489C22⋊C4#63811yescharacteristic
490C22⋊C4#63811yescharacteristic
491C42—181no—
492C42C22×C3⋊D311yescharacteristic
493C22×C3—24no—
494C22×C3—24no—
495C22×C3—28no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3C22×#6714yes—
503C2×D3—124no—
504C2×D3—124no—
505C2×D3—124no—
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—24no—
510C3×C4—44no—
511C3×C4—44no—
512C3×C4—44no—
513C3×C4C2×D3×D414yes—
514C3×C4#100414yes—
515Dic3—68no—
516Dic3—124no—
517Dic3—124no—
518C32#326911yescharacteristic, complemented, Sylow
519C23—21no—
520C23—181no—
521C23C2×#63811yescharacteristic
522C23C2×#63811yescharacteristic
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—92no—
528Q8—181no—
529Q8—181no—
530Q8—181no—
531Q8—362no—
532D4—21no—
533D4—41no—
534D4—42no—
535D4—42no—
536D4—181no—
537D4—181no—
538D4—362no—
539D4—362no—
540D4D4×C3⋊D312yes—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—362no—
555C2×C4—362no—
556C2×C4C2×#63811yescharacteristic
557C2×C4C2×#63811yescharacteristic
558C2×C4C2×#63811yescharacteristic
559C2×C4C2×#63811yescharacteristic
560C2×C4C23×C3⋊D311yescharacteristic
561C8—92no—
562C8—181no—
563C8—181no—
564C8—181no—
565C2×C3—44no—
566C2×C3—44no—
567C2×C3—48no—
568C2×C3D4×#6714yes—
569C2×C3#582214yes—
570C2×C3#583814yes—
571D3—244no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—41no—
580C22—41no—
581C22—361no—
582C22—361no—
583C22—361no—
584C22C22×#63811yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—182no—
593C4—361no—
594C4—361no—
595C4C2×D4×C3⋊D311yescharacteristic
596C4#6436111yescharacteristic
597C3#8352814yescomplemented
598C2—41no—
599C2—41no—
600C2—42no—
601C2—721no—
602C2D4×#63811yescharacteristic
603C2#1059629311yescharacteristic
604C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#547C2
socleC22×C32C22×D4
hypercenter#547C3⋊D3
hypocenterC32#3269
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×#547C2semidirect
2. C2×#64160C2semidirect
3. C2×#64159C2semidirect
4. #10596023C2semidirect
5. #10592938C2semidirect
6. #10592937C2semidirect
7. #10592789C2semidirect
8. #10592785C2semidirect
9. #10592750C2semidirect
10. #10592749C2semidirect
11. #10592748C2semidirect
12. #10592746C2semidirect
13. #10592717C2semidirect
14. #10592715C2semidirect
15. #10592710C2semidirect
62. C3×#547D3semidirect
124. #3754D4semidirect
234. #547C3⋊D3semidirect
518. C32#3269semidirect
597. C3#83528semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5472
C2×#641602
C2×#641592
#105960232
#105929382
#105929372
#105927892
#105927852
#105927502
#105927492
#105927482
#105927462
#105927172
#105927152
#105927102
#835283